Chapter 2.3, Problem 63E

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The Intermediate Value Theorem guarantees that f(a) and f(b) differ in sign when a continuous function f has at least one zero on [a, b].

[Ex8 Q2] Calculus question about continuity :)

Analyze continuity of the function.

ASAP

Determine if the statement is true or false. Provide a counterexample or proof.  Suppose f is a continuous injective function, and f-1 is differentiable, then f is also differentiable.

mathmatics prove that f(x)=3x+1 is continuous in all points.

Identify whether these statements are SOMETIMES TRUE, ALWAYS TRUE or NEVER TRUE, show your Complete Explanations (This is all about Calculus: Continuity and Differentiability of a Function). a. If a function is differentiable at a point, then it is continuous at the same point. (Explain WHY) b. If a function is continuous at a point, then it is differentiable at the same point. (Explain WHY) c. If a function is differentiable at a point, then it is not continuous at the same point (Explain WHY) d. If a function is not differentiable at a point , then it is continuous at the same point. (Explain WHY) e. If function is not differentiable at a point, then it is not continuous at the same point. (Explain WHY) I already provided the answers I just need the COMPLETE EXPLANATIONS.a. ALWAYS TRUEb. SOMETIMES TRUEc. NEVER TRUEd. SOMETIMES TRUEe. SOMETIMES TRUE

Study the continuity of the functions in the points mentioned

Determine the continuity of the function at the given points. for x 1 f(x) = [1, at x = 1 and x = 0 for x +1 4+ 3 2+ 1+ 十 -4 -3 -1- 3. -2 -3+ 4-